Geometry: Polygons and Circles

Define key terms related to polygons and circles.

Calculate the area and perimeter of common polygons (triangles, rectangles, parallelograms).

Calculate the area and circumference of a circle.

State and apply the Pythagorean Theorem.

The Geometry of Shapes

A polygon is a closed plane figure with three or more straight sides.

Perimeter: The total distance around the outside of a polygon; the sum of its side lengths.

Area: The amount of two-dimensional space a polygon occupies.

Common Area Formulas:

Rectangle: Area = length × width

Parallelogram: Area = base × height

Triangle: Area = ½ × base × height

Trapezoid: Area = ½ × (base₁ + base₂) × height

The Pythagorean Theorem:

For any right triangle with legs a and b and hypotenuse c (the side opposite the right angle):

a² + b² = c²

This is one of the most fundamental theorems in geometry.

A circle is the set of all points in a plane that are at a fixed distance (the radius) from a fixed point (the center).

Radius (r): The distance from the center to any point on the circle.

Diameter (d): The distance across the circle through the center. d = 2r.

Circumference (C): The distance around the circle (its perimeter).

C = 2πr or C = πd

Area (A): The space enclosed by the circle.

A = πr²

Pi (π): An irrational constant, approximately 3.14159, representing the ratio of a circle's circumference to its diameter.

Polygon: A plane figure with at least three straight sides and angles, and typically five or more.
Pythagorean Theorem: A fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (a² + b² = c²).
Circle: A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
Circumference: The enclosing boundary of a curved geometric figure, especially a circle.
Radius: A straight line from the center to the circumference of a circle or sphere.